SOLUTION: A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, fin

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Question 1198595: A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, find the total area and volume of the cone. The volume of the solid generated by this triangle may be expressed as V= βπ/σ √γ 〖in〗^3 where β and σ are positive integers and γ is a prime number. Find the smallest sum of β, γ, and σ.
Answer by mananth(16946) (Show Source):
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A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, find the total area and volume of the cone.

The central angle is 120 deg
radius = 20 in
length of arc = *2*pi*r
= 120/360 *2*20*pi
=40 *pi/3
When it is rolled into a cone the radius beomes the slant height and length of arc beomes circumference 0f the base of cone
2*pi*r = 40 *pi/3
r = 40/6 =20/3
height = sqrt(20^2-(20/3)^2 )
Volume of cone = 1/3 pi*r^2
height of cone = sqrt(20^2-(20/3)^2)
height h =
radius r=20/3
slant height l=20
Find volume and Total surface area